Refined asymptotics for Landau-de Gennes minimizers on planar domains

In our previous work [12], we studied asymptotic behavior of minimizers of the Landau-de Gennes energy functional on planar domains as the nematic correlation length converges to zero. Here we improve upon those results, in particular by sharpening the description of the limiting map of the minimizers. We also provide an expression for the energy valid for a small, but fixed value of the nematic correlation length. In this paper we revisit some of the conclusions we obtained in [12]. In that paper we considered the Landau-de Gennes energy functional, which can be expressed as

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